JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://raw.github.com/fgelinas/timepicker/master/jquery.ui.timepicker.js"></script>
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.9/themes/base/jquery-ui.css">
<div id="withModal">
    <input type="button" id="modalButton" value="Open Modal"/>
    
    <div style="display: none;" id="modal">
        <input id="timepicker-modal" type="text"/>
    </div>
</div>

<div id="without">
    <input id="timepicker" type="text"/>
</div>

CSS

/*
 * Timepicker stylesheet
 * Highly inspired from datepicker
 * FG - Nov 2010 - Web3R 
 *
 * version 0.0.3 : Fixed some settings, more dynamic
 * version 0.0.4 : Removed width:100% on tables
 * version 0.1.1 : set width 0 on tables to fix an ie6 bug
 */

.ui-timepicker-inline { display: inline; }

#ui-timepicker-div { padding: 0.2em; background-color: #fff; }
.ui-timepicker-table { display: inline-table; width: 0; }
.ui-timepicker-table table { margin:0.15em 0 0 0; border-collapse: collapse; }

.ui-timepicker-hours, .ui-timepicker-minutes { padding: 0.2em;  }

.ui-timepicker-table .ui-timepicker-title { line-height: 1.8em; text-align: center; }
.ui-timepicker-table td { padding: 0.1em; width: 2.2em; }
.ui-timepicker-table th.periods { padding: 0.1em; width: 2.2em; }

/* span for disabled cells */
.ui-timepicker-table td span {
    display:block;
    padding:0.2em 0.3em 0.2em 0.5em;
    width: 1.2em;

    text-align:right;
    text-decoration:none;
}
/* anchors for clickable cells */
.ui-timepicker-table td a {
    display:block;
    padding:0.2em 0.3em 0.2em 0.5em;
    width: 1.2em;
    cursor: pointer;
    text-align:right;
    text-decoration:none;
}


/* buttons and button pane styling */
.ui-timepicker .ui-timepicker-buttonpane {
    background-image: none; margin: .7em 0 0 0; padding:0 .2em; border-left: 0; border-right: 0; border-bottom: 0;
}
.ui-timepicker .ui-timepicker-buttonpane button { margin: .5em .2em .4em; cursor: pointer; padding: .2em .6em .3em .6em; width:auto; overflow:visible; }
/* The close button */
.ui-timepicker .ui-timepicker-close { float: right }

/* the now button */
.ui-timepicker .ui-timepicker-now { float: left; }

/* the deselect button */
.ui-timepicker .ui-timepicker-deselect { float: left; }


/* IE6 IFRAME FIX (taken from datepicker 1.5.3 */
.ui-timepicker-cover {
    display: none; /*sorry for IE5*/
    display/**/: block; /*sorry for IE5*/
    position: absolute; /*must have*/
    z-index: -1; /*must have*/
    filter:...

JavaScript

$("#timepicker-modal").timepicker();
$("#timepicker").timepicker();

    $("#modal").dialog({
        modal: true,
        autoOpen: false,
        title: "modal test"
    });

$("#modalButton").click(function() {
    $("#modal").dialog('open');
});